Table 3 Description of the closed testing procedure for updating of multinomial logistic regression models

1. Original model vs refitting

H0: both models have the same fit, log L _original = log L _refitted.

Test: likelihood ratio test with (q + 1) × (k − 1)df.

Result: if H0 not rejected, choose the original model, else go to step 2.

2. Intercept recalibration vs refitting

H0: both models have the same fit, log L _int recal = log L _refitted.

Test: likelihood ratio test with q × (k − 1)df.

Result: if H0 not rejected, choose intercept recalibration, else go to step 3.

3. Logistic recalibration vs refitting

H0: both models have the same fit, log L _logrecal = log L _refitted.

Test: likelihood ratio test with (q − k + 1) × (k − 1)df.

Result: if H0 not rejected, choose logistic recalibration, else choose refitting.